Question

Cho tam giác ABC điểm M trên cạnh BC sao cho MB = 3MC , Hãy phân tích vecto\(\overrightarrow{AM}\) theo 2 vecto \(\overrightarrow{u}=\overrightarrow{AB},\overrightarrow{v}=\overrightarrow{AC}\)

Answer 1

\(\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}\Rightarrow\overrightarrow{BC}=\overrightarrow{AC}-\overrightarrow{AB}=\overrightarrow{v}-\overrightarrow{u}\)

\(\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}=\overrightarrow{AB}+\frac{3}{4}\overrightarrow{BC}=\overrightarrow{u}+\frac{3}{4}\left(\overrightarrow{v}-\overrightarrow{u}\right)=\frac{1}{4}\overrightarrow{u}+\frac{3}{4}\overrightarrow{v}\)